The invention is based on a fuel injection pump as generally defined hereinafter. In a known fuel injection pump of this kind (U.S. Pat. No. 2,147,390), the control slide has oblique control edges on its upper and lower end edges; the upper control edge, by the entry of the lower control bore extending in the pump piston determines the supply onset and the upper control edge, by the emergence of the upper control bore extending in the pump piston determines the end of supply. As a result, the control slide becomes relatively long in structure, which is a considerable disadvantage in slide-controlled fuel injection pumps, which are already relatively large. Furthermore, an extra impact plate must be provided opposite the mouth of the upper control bore where it emerges from the control slide. A further disadvantage in terms of filling the pump work chamber during the intake stroke is that a control bore can only be opened near bottom dead center; given the relatively low filling pressures at high rpm, either this can lead to an inadequate filling of the pump work chamber, or it necessitates relatively large control bore cross sections, with the disadvantages of a larger idle volume in the first instance and a dependency of the control quality on the rpm in the second, the latter because the cross section varies over time on account of the relatively large control bore cross section.